Unit 33 Congruence and Similarity

Unit 33Congruence and Similarity

Presentation 1 Tests for Congruence

Presentation 2 Congruent Triangles

Presentation 3 Similar Shapes

Presentation 4 Similar Triangles

Presentation 5 Line, Area and Volume Ratios

Unit 3333.1 Tests for Congruence

Test 1 (side, side side)

If all three sides of one triangle are the same as the lengths of the sides of the second triangle, then the two triangles are congruent

This is referred to as SSS.?

Test 2 (side, angle, side)

If two sides of one triangle are the same length as two sides of the other and the angle between these two sides is the same in both triangles, then the triangles are congruent.

This is referred to as SAS.?

Test 3 (angle, angle, side)

If two angles and the length of one side are the same in both triangles then they are congruent.

This is referred to as AAS.?

Test 4 (right angle, hypotenuse, side)

If both triangles contain a right angle, have hypotenuses of the same length and one other side of the same length, then they are congruent.

This is referred to as RHS.?

Unit 3333.2 Congruent Triangles

ABC and GHI ?

In each of the following, which triangles are congruent

ABC and DEF and JKL?

In each of the following, which triangles are congruent

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ABC and DEF and JKL?

In each of the following, which triangles are congruent

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Unit 3333.3 Similar Shapes

Which of these shapes are similar to shape A?

CDEGHI?

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Unit 3333.4 Similar Triangles

What is:(a) the length of CB. 5cm(b) the length of IJ. 12.5cm(c) the size of angle PQR. 65°(d) the size of angle ABC. 65°?

Triangles ABC, PQR and HIJ are all similar.

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Unit 3333.5 Line, Area and Volume

Ratios

The diagram shows two similar cuboids

Volume of cuboid A = 60cm³Volume of cuboid B = 480cm³ Surface area of cuboid A = 94cm²Surface area of cuboid B = 374cm²

Lengths increase by a factor of 2Areas increase by a factor of 4 = 2²Volumes increase by a factor of 8 = 2³

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